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A324222 a(n) is defined by the condition that the decimal expansion of Sum_{n>0} 1/a(n)^n = 1/a(1)^1 + 1/a(2)^2 + 1/a(3)^3 + ... begins with the concatenation of these numbers; also a(1) = 3 and a(n) > a(n-1). 9
3, 6, 14, 75, 574, 2029, 4589, 7927, 78325, 681667, 720945 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
a(11) is the last term because the sequence cannot be extended. At any step a(n) is chosen as the least number greater than a(n-1) that meets the requirement. Up to 720945 the sum is 0.3 6 14 75 574 2029 4589 7927 78325 681667 720945 0664... and the zero after 720945 cannot be removed.
If the limitation a(n) > a(n-1) were removed then the sequence would be 3, 6, 14, 75, 57, 58, 91, 197, 53, 423, 613, 102, 956 and 956 would be the last term because after it the sum presents 0316... and the zero cannot be removed. - Giovanni Resta, Feb 20 2019
LINKS
EXAMPLE
1/3^1 = 0.3333...
1/3^1 + 1/6^2 = 0.36111...
1/3^1 + 1/6^2 + 1/14^3 = 0.3614755...
The sum is 0.3 6 14 75 574 ...
MAPLE
P:=proc(q, h) local a, b, d, n, t; a:=1/h; b:=ilog10(h)+1;
d:=h; print(d); t:=2; for n from 1 to q do
if trunc(evalf(a+1/n^t, 100)*10^(b+ilog10(n)+1))=d*10^(ilog10(n)+1)+n
then b:=b+ilog10(n)+1; d:=d*10^(ilog10(n)+1)+n; a:=a+1/n^t; t:=t+1;
print(n); fi; od; end: P(10^5, 3);
CROSSREFS
Sequence in context: A257320 A318344 A129090 * A058141 A144654 A132279
KEYWORD
nonn,base,fini,full
AUTHOR
Paolo P. Lava, Feb 18 2019
EXTENSIONS
a(7)-a(11) added by Giovanni Resta, Feb 20 2019
STATUS
approved

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Last modified March 29 10:59 EDT 2024. Contains 371277 sequences. (Running on oeis4.)